The algorithm method used for the 3d-reconstruction. e.g. Random-conical reconstruction: a method of data collection and reconstruction used for single particles, typically used initially in a project, to obtain a first low-resolution reconstruction of the macromolecule [Radermacher et al., 1987]. Two images of the same specimen field are collected, one with untilted grid, the other with the grid tilted by 50 to 60 degrees. Any set of particles presenting the same view in the untilted-specimen image form a random-conical projection set in the associated tilted-specimen image. Helical reconstruction Helical reconstruction is used when the protein of interest forms a natural helix. Since the helix is a recurring structure with a very well defined pattern, the repeating pattern of the helix can be exploited to solve the structure. In this case, no alignment of the particles is needed, since the individual positions of subunits within the helix are clearly defined by the shape of the helix. Two common examples of structures solved by helical reconstruction are TMV and microtubules. Icosahedral reconstruction Icosahedral reconstructions also take advantage of internal symmetry and repetition to generate a detailed three-dimensional structure from the data set. In this case, the symmetry is icosahedral (twenty-one sided). Many viruses exhibit icosahedral symmetry in their capsid proteins, and this method has been used to solve their structures. Electron crystallography Electron crystallography is similar to x-ray crystallography in that it exploits the repeating pattern found within a crystal to generate a structure. Just as with x-ray crystallography, difraction patterns are generated and are used to define an electron density map. However, it differs in that the crystal used is a two-dimensional sheet as opposed to three three-dimensional crystals of x-ray crystallography. Common Lines Another reconstruction method searches for the intersection of any two projections in Fourier space. The Fourier transform of the experimental projections all form slices around a common core in Fourier space. Therefore, the intersection of these projections are unique (unless the projections perfectly overlap), and their relative orientation can be found when three or more projections are used. A principal problem with this method is that the handedness of the image is lost. This, however, can later be corrected by visual examination of the model with other known structural information. Back Projection As its name implies, back projection is the inverse function of projection. When an n-dimensional object is projected, each projection is an n-1 dimensional sum of its density along the projection axis. Therefore, a sphere would have circles as its projections. A cube, on the other hand, would produce either squares, diamonds, or other intermediate parallelograms depending on the direction of projection. The actual shape, of course, depends on the orientation from which the projection was made. The reverse function is called back projection and regenerates the original object.